How to make two separate curves move together
With the Hook modifier you can parent the vertices of 2 separate curves to the same empties or bones.
If you want to parent a curve vertex to a bone:

Disable the Lock Object Mode option:



Select the bone in Pose mode, shift select the curve, go in Edit mode, select the vertex, press CtrlH &gt; Hook to Selected Object Bone:



It has automatically created a Hook modifier for the curve:


Move the bone, it will move the vertex, the advantage compared to a hook to empty is that you can always come back to the bone rest pose:


To hook to an empty you just need to select the curve vertex and CtrlH &gt; Hook to New Object, it will automatically create a new empty:


Now you can hook the vertices of the other curve to the same bones or empties.